Mathematical statistical models and qualitative theories for economic and social sciences
Studies in Systems, Decision and Control 104
Šárka Hošková-Mayerová Fabrizio Maturo Janusz Kacprzyk Editors
MathematicalStatistical Models and Qualitative Theories for Economic and Social Sciences
Studies in Systems, Decision and Control Volume 104
Series editor Janusz Kacprzyk, Polish Academy of Sciences, Warsaw, Poland e-mail: email@example.com
About this Series The series “Studies in Systems, Decision and Control” (SSDC) covers both new developments and advances, as well as the state of the art, in the various areas of broadly perceived systems, decision making and control- quickly, up to date and with a high quality. The intent is to cover the theory, applications, and perspectives on the state of the art and future developments relevant to systems, decision making, control, complex processes and related areas, as embedded in the ﬁelds of engineering, computer science, physics, economics, social and life sciences, as well as the paradigms and methodologies behind them. The series contains monographs, textbooks, lecture notes and edited volumes in systems, decision making and control spanning the areas of Cyber-Physical Systems, Autonomous Systems, Sensor Networks, Control Systems, Energy Systems, Automotive Systems, Biological Systems, Vehicular Networking and Connected Vehicles, Aerospace Systems, Automation, Manufacturing, Smart Grids, Nonlinear Systems, Power Systems, Robotics, Social Systems, Economic Systems and other. Of particular value to both the contributors and the readership are the short publication timeframe and the world-wide distribution and exposure which enable both a wide and rapid dissemination of research output.
More information about this series at http://www.springer.com/series/13304
Šárka Hošková-Mayerová Fabrizio Maturo ⋅ Janusz Kacprzyk Editors
Mathematical-Statistical Models and Qualitative Theories for Economic and Social Sciences
Editors Šárka Hošková-Mayerová Department of Mathematics and Physics, Faculty of Military Technology University of Defence Brno Czech Republic
Janusz Kacprzyk Systems Research Institute Polish Academy of Sciences Warsaw Poland
Fabrizio Maturo Department of Business Administration University “G. d’Annunzio” of Chieti-Pescara Pescara Italy
The book “Mathematical-Statistical Models and Qualitative Theories for Economic and Social Sciences” is part of the important series “Studies in Systems, Decision and Control” published by Springer. This is the result of a scientiﬁc collaboration, in the ﬁeld of economic and social systems, among experts from “University of Defence” in Brno (Czech Republic), “G. d’Annunzio” University of Chieti-Pescara (Italy), “Pablo de Olavide” University of Sevilla (Spain), and “Ovidius University” in Constanţa, (Romania). The variety of the contributions developed in this volume reflects the heterogeneity and complexity of economic and social phenomena; thus, in this book, there is a convergence of many research ﬁelds, such as statistics, decision making, mathematics, complexity, psychology, sociology, and economics. The different studies included in this book, selected using a peer-review process, present also empirical interesting researches conducted in various countries. Each chapter was peer-reviewed by two independent referees (e.g., J. Beránek, J. Čermák, D. Řezáč, and V. Voženílek, (CZ); M. Grega, S. Filip, and J. Klučka (SK); A. Porrovecchio (FR); N. Bortoletto, M. Squillante, and A. Ventre, (IT); E. Barrera Algarín, O. Vazquez-Aguado, and C.M. Vicente (ES)). The volume is divided into two parts: The ﬁrst one is “Recent Trends in Mathematical and Statistical Models for Economic and Social Sciences,” whereas the second one is “Recent Trends in Qualitative Theories for Economic and Social Sciences.” Part I collects research of scholars and experts on quantitative matters, who propose mathematical and statistical models for social sciences, economics, ﬁnance, and business administration. The book opens with the contribution of Veronika Mitašová, Ján Havko, and Tomáš Pavlenko. They propose a study titled “Correlational Research of Expenditure Spend on Slovak Armed Forces Participation in Peace Support Operations Led by NATO” in which a multifactor single-equation econometric model is created and tested. Salvador Cruz Rambaud, Fabrizio Maturo, and Ana María Sánchez Pérez aim to develop three approaches for obtaining the value of an n-payment annuity, with payments of one unit each, when the interest rate is random. To calculate the value v
of these annuities, the authors assume that only some non-central moments of the capitalization factor are known. The ﬁrst technique consists in using a tetra parametric function which depends on the arctangent function. The second expression is derived from the so-called quadratic discounting, whereas the third approach is based on the approximation of the mathematical expectation of the ratio of two random variables by Mood et al. (1974). A comparison of these methodologies through an application, using the R statistical software, shows that all of them lead to different results. Josef Navrátil and Veronika Sadovská concentrate on the health risk assessment of selected pollutants derived from residential ﬁre simulated in ﬁre container. The key interest of their study is dedicated to polycyclic aromatic hydrocarbons (PAHs) and their toxicity and harmful effects on the health of ﬁreﬁghters, whose protection by breathing apparatus is insufﬁcient. Qualitative and quantitative comparison of the results of the entrance draft tests and the entrance tests of mathematics is illustrated by Radovan Potůček. His contribution focuses on the applicants for the bachelor and master study at the Faculty of Military Technology of the University of Defence in Brno. He refers to tests organized by the Department of Mathematics and Physics and presents the results of the applicants (from the military secondary school and civilian secondary schools), comparing and evaluating them from the qualitative and quantitative point of view. Recent trends in digital ethnography are presented by Vanessa Russo. She shows theories, models, and case studies with the aim of deﬁning the boundaries of digital ethnography. Finally, with the help of the comparison between empirical cases, she tries to understand critical points, limits, and research prospects for digital ethnographers. Lenka Hrbková, Jozef Zagrapan, and Roman Chytilek analyze the demand side of negativity and privatization in news with an experimental study of news consumer habits. They remark that negativity in media and emphasis on personal side of politics are often cited as a common journalist practice, which is harmful to democratic processes. Journalists and media houses are often held accountable for these phenomena because they prioritize proﬁt over the quality of content. Then, they offer an analysis focused on demand side of both negativity and privatization of political news. Using the Dynamic Process Tracing Environment (DPTE), they test the assumption that both of these features of political media coverage may be driven by audience demand for negative and personal news. Martin Hubacek and Vladimir Vrab propose a constructive simulation for cost assessment of training. They highlight that constructive simulation, which is used as a tool for training of commanders and staffs of military units, has important beneﬁts for a higher quality of training. Furthermore, constructive simulation gradually penetrates into other spheres such as the training of emergency staff. However, relevant studies about the economical beneﬁts of the use of constructive simulation for training are relatively rare. The presented cost comparison of the exercises is based on the authors’ experience gained during the implementation of various types
of exercise, at the Center of Simulation and Training Technologies of Brno, with the use of constructive simulation OneSAF. Social problems and decision making for teaching approaches and relationship management in an elementary school are the topics of interest of Luciana Delli Rocili and Antonio Maturo. Their chapter illustrates teaching experiences in the primary school and applications of theories regarding the choice of teaching methods in this particular context. In order to decide the most appropriate intervention strategies, both in terms of teaching and for an efﬁcient management of relationships within the class and with the students’ families, they consider that the ﬁrst step is to discover the students’ social and environmental background. The experience described herein is at the basis of the ﬁnal proposal on how to concretely implement some decisional procedures at school, as for instance those linked to the limited rationality and the analytic hierarchy process theorized by Saaty. Ferdinando Casolaro and Alessandra Rotunno propose a chapter titled “From the pictorial art to the linear transformations.” In particular, the authors suggest a path for the teaching of geometry in Italy that reflects the development, which took place over the past two centuries. Moreover, they highlight the social aspects of a teaching based on the graphical visualization as required by the projective geometry. Bekesiene, Hošková-Mayerová, and Diliunas focus on the identiﬁcation of effective leadership indicators in army forces of Lithuania. They remark that leadership is of overriding importance in the military sphere because the foundation for leading a unit consists in influence, motivation, and soldiers’ inspiration by the leader’s personal example. The Lithuanian Army seeks to develop a military leadership identity as a way to promote mission success. This study is sought to identify the effective leadership style, which is appreciated by soldiers in the Lithuanian Armed Forces. The authors adopt the Leader Behavior Description Questionnaire (LBDQ) for measuring the behavior of leaders. The data collected from military personnel, holding different ranks and doing their professional military service of all the units of the Lithuanian Armed Forces, were analyzed using structural equation models (SEM). “Why We Need Mathematics in Cartography and Geoinformatics” is the title of the chapter of Václav Talhofer. He highlights that mathematics is necessary for understanding of many procedures that are connected to modeling of the Earth as a celestial body, to ways of its projection into a plane, to methods and procedures of modeling of landscape and phenomena in society, and to visualization of these models in the form of electronic as well as classic paper maps. Not only general mathematics, but also its extension of differential geometry of curves and surfaces, ways of approximation of lines and surfaces of functional surfaces, mathematical statistics, and multicriteria analyses seem to be suitable and needful. Moreover, he suggests that the underestimation of the signiﬁcance of mathematical education in cartography and geoinformatics is inappropriate and lowers competences of cartographers and geoinformaticians to solve problems. Hana Svatoňová and Radovan Šikl investigate the cognitive aspects of interpretation of image data. Interpretation of image data is a complex of complicated
intellectual operations, which is based on visual. The theoretical part of their study summarizes the scientiﬁc knowledge of processes of visual perception applied in the process of visual interpretation of satellite, aircraft, and map image data. Author presents partial phases of image data interpreting process: from the initial recording of the image to detection, identiﬁcation, and objects classiﬁcation. The complexity of the cognitive process with regard to biological and psychological characteristics of the individual is highlighted. The research section presents the results of image data interpretation research according to gender of individuals/research respondents. Engin Baysen, Šárka Hošková-Mayerová, Nermin Çakmak, and Fatma Baysen study the misconception regarding providing citations. Their research aims at ﬁnding out citation understandings of Czech and Turkish secondary and high school students. Except for few students, secondary and high school students have misconceptions concerning providing citations. Students are unintentionally vulnerable to plagiarize while reporting. The study shows that only secondary and high school education is not enough for implementing honesty regarding citation. Therefore, the authors remark the importance of educating and informing students about honesty in research and plagiarism. Subjective preconditions and objective evaluation of interpretation of image data are analyzed in the chapter of Hana Svatoňová and Šárka Mayerová-Hošková. In learning and teaching, there is an ongoing teaching relationship with speciﬁc and bidirectional relations between the teacher and student. Teacher can have either a strongly positive or, on the contrary, a strongly negative impact via his communication and interactions with students. From the wide idea of attitudes and values that constitute the relationship between the teacher and the student, their article is focused on a part of subjective assumptions about the success of students in a speciﬁc task: in this case, interpretation of aerial and satellite images and maps. The respondents of the researcher were elementary school teachers and students aged between 11 and 15. The subjective assumptions of teachers were compared with assumptions of students, and subsequently, all subjective assumptions were compared with objective data. Fabrizio Maturo, Stefania Migliori, and Francesco Paolone analyze the influence of institutional and foreign shareholders on national board diversity of companies. Investigating the external antecedents of board diversity, they suggest the use of functional data analysis for diversity assessment in corporate governance studies. Focusing on a sample of 1230 Italian medium–large ﬁrms, their results show that institutional shareholders do not influence national board diversity, while foreign shareholders strongly affect it, especially when they hold more than 50% of shares. Thus, the authors address the research gap on the determinants of national board diversity and enrich comparative European research on this topic. Francesco Paolone and Matteo Pozzoli investigate the effect of ﬁnancial crisis of Earnings Manipulation by adopting the Beneish model. Speciﬁcally, empirical evidence from the “Top World Enterprises,” ranked by “Sales Revenues” in the ﬁscal year 2013, is presented. Their results show that there has been a greater propensity for manipulating earnings in the ﬁrst year of the global crisis:
Companies have had a tendency to increase creation of social wealth, in terms of generating higher proﬁts. This would mean that the crisis has had a positive effect on handling of income by the largest companies in the world because the crisis itself has restricted the earnings manipulation policies. Reasoning and decision making in practicing counseling are considered by Antonio Maturo and Antonella Sciarra. The counseling procedure is considered as a dynamical decision-making problem, where the awareness of alternatives and objectives and their evaluations are maieutically induced by the counselor. After presenting some relevant practices of counseling and related decision-making procedures, this study shows the use of the mathematical theory of decisions for a formalization of the counseling methods, in order to model, clarify, and make rigorous procedures of decision. Finally, it is shown that fuzzy reasoning can give a useful formal help to the task of the counselor because of its flexibility. Ana Vallejo Andrada, Šárka Hošková-Mayerová, José Luis Sarasola Sanchez-Serrano, and Josef Krahulec deal with how society views the current wave of migration, speciﬁcally in Andalusia (Spain) and Czech Republic. The problem is described in a pre-case study, which covers results concerning citizens’ approach to an urgent social topic, i.e., migration and immigration and risks related to these questions. First, the research presents a summary about the history of migrations in both regions; then, the current situation in those regions is characterized; after that, the questionnaire was prepared with the idea of how people feel this phenomenon, and survey was made. Finally, based on the results, possible risks are presented and some strategies on how to deal with inconvenient situations, which might arise, are suggested. Domenico Di Spalatro, Fabrizio Maturo, and Lorella Sicuro face the issue of inequalities in the provinces of Abruzzo making a comparative study through the indices of deprivation and principal component analysis. The indices of deprivation are a valuable tool to measure the socioeconomic disadvantage in certain geographical areas of interest. This study aims to compare inequalities between the provinces of Abruzzo over the last two decades suggesting some indices of deprivation to capture the key aspects of the great wealth of information relating to population census. Speciﬁcally, they propose three indices of deprivation to measure the material and social disadvantage. Moreover, a principal component analysis is performed using the most known indicators of deprivation. Using these methods, their results show an increase in the proportion of disadvantaged areas in the Abruzzo region from 1991 to 2011 in its four provinces. Part II “Recent Trends in Qualitative Theories for Economic and Social Sciences” collects research of scholars and experts on qualitative matters, who propose and discuss on social, economic, and teaching issues. Part II opens with the chapter of Grazia Angeloni which highlights the reasons why educational institutions should be considered complex systemic organizations. Speciﬁcally, she suggests a multidisciplinary approach tending to make use, on the one hand, of different lenses, in order to appreciate the organizational phenomenon taken into consideration, and on the other, it is an effort to join different epistemes for practical purposes.
Jose Luis Sarasola Sánchez-Serrano, Ana Vallejo Andrada, and Alberto Sarasola Fernandez in their study “Sociability and Dependence” illustrate the results of a survey conducted for studying elders sociability in the urban area and its relation with the dependency degree. Stefania Fantinelli presents her research titled “Knowledge Creation Processes Between Open Source Intelligence and Knowledge Management.” She adopts some interviews on a sample of Italian analysts and experts to reveal what is the common use of “Open Source Intelligence” methods and how they are linked to the knowledge creation and knowledge management processes. Furthermore, she explores this method in a social psychology perspective and in relation to knowledge management in organizations. Advanced technologies for social communication are proposed by Roberto Salvatori, who highlights the speed of change and spread of ICT in Education, which put the entire educational system in the position of continuously redesigning new methods and teaching models adapted to a globalized and interconnected society, where knowledge is distributed, easily accessible, and constantly updated. Valentina Savini deals with the concept of social distance as an interpretation of a territory. She shows that the physical and spatial aspects of social distance identiﬁed by Simmel disappeared from the theoretical setting when the issue was analyzed in America. Moreover, the approaches that combine the physical and relational dimensions, based on Italian and English sociologists of the last few years, should be preferred. Gabriele Di Francesco presents a socio-vital areas analysis with a qualitative approach to sociological analysis of urban spaces and social life. He presents the theoretical synthesis and the technical and methodological setting of a research, aimed to analyzing and evaluating the urban places and spaces of social life, where the human interactions take place and the city come to life. Cultural and natural heritage challenges are illustrated by Zdena Rosická. The author remarks that every cultural heritage object and its content has its unique character and calls for an individual approach considering safety, protection, security, risk-preparedness, and further viable use. The public usually know about high-value losses of cultural property caused by burglary, ﬁre of flood when the mass media report them; however, physical care, including environmental and conservation control, property transfer and transport, personal access, thefts from exhibits during the day, and incidents of smash bring about higher-cost internal losses, which are sometimes not reported at all. In case any disaster strikes, harm to cultural treasure is sometimes serious and losses irreplaceable unless relevant measures are taken in time. Fiorella Paone aims to contribute to reflection about new form of emerging literacy starting from communicational changes, which characterize new social and cultural paradigm due to the use of electronic media. The narrative paradigm thought as linguistic practice of construction of liquid identities is considered as a possible operative strategy able to promote personal development in a holistic perspective, enforcing both personal and social self.
Vincenzo Corsi takes into account the sociological methods and construction of local welfare in Italy. He describes the importance of the study of the social care needs of the population for the construction of the local welfare system. Then, he shows some aspects of the local welfare system in Italy. Daniel Flaut and Enache Tuşa analyze some aspects of social life in Romanian villages in the interwar period. At the same time, they describe the standard of living in rural areas, which varied depending on the ethnicity of the residents, using examples taken from the Dobrudja region. A large spectrum of problems related to statistics, mathematics, teaching, social science, and economics has been presented in this volume. Therefore, a broad range of tools and techniques that may be used to solve problems on these topics has been presented in detail in this book, which is an ideal reference work for all those researchers interested in recent quantitative and qualitative tools. Due to the wide range of topics of the research results collected in this book, it is addressed, in equal measure, to mathematicians, statisticians, sociologists, philosophers, and specialists in the ﬁelds of communication, social, and political sciences. Brno, Czech Republic Pescara, Italy Warsaw, Poland July, 2017
Šárka Hošková-Mayerová Fabrizio Maturo Janusz Kacprzyk
Part I 1
Recent Trends in Mathematical and Statistical Models for Economic and Social Sciences
Correlational Research of Expenditure Spend on Slovak Armed Forces Participation in Peace Support Operations Led by NATO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Veronika Mitašová, Ján Havko and Tomáš Pavlenko Health Risk Assessment of Combustion Products from Simulated Residential Fire . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Josef Navrátil, Veronika Sadovská and Irena Švarcová
Qualitative and Quantitative Comparison of the Entrance Draft Tests and the Entrance Tests Results in Mathematics . . . . . . Radovan Potůček
Digital Ethnography Theories, Models and Case Studies . . . . . . . . Vanessa Russo
The Demand Side of Negativity and Privatization in News: Experimental Study of News Consumer Habits . . . . . . . . . . . . . . . . Lenka Hrbková, Jozef Zagrapan and Roman Chytilek
Cost Assessment of Training Using Constructive Simulation . . . . . Martin Hubacek and Vladimir Vrab
Social Problems and Decision Making for Teaching Approaches and Relationship Management in an Elementary School . . . . . . . . . Luciana Delli Rocili and Antonio Maturo
From the Pictorial Art to the Linear Transformations . . . . . . . . . . Ferdinando Casolaro and Alessandra Rotunno
Identiﬁcation of Effective Leadership Indicators in the Lithuania Army Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S. Bekesiene, S. Hoskova-Mayerova and P. Diliunas
10 Why We Need Mathematics in Cartography and Geoinformatics? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Václav Talhofer
11 Cognitive Aspects of Interpretation of Image Data . . . . . . . . . . . . . Hana Svatoňová and Radovan Šikl 12 Misconceptions Regarding Providing Citations: To Neglect Means to Take Risk for Future Scientiﬁc Research . . . . . . . . . . . . . Engin Baysen, Sarka Hoskova-Mayerova, Nermin Çakmak and Fatma Baysen 13 Social Aspects of Teaching: Subjective Preconditions and Objective Evaluation of Interpretation of Image Data . . . . . . . Hana Svatoňová and Šárka Hošková-Mayerová 14 Do Institutional or Foreign Shareholders Inﬂuence National Board Diversity? Assessing Board Diversity Through Functional Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F. Maturo, S. Migliori and F. Paolone 15 Inequalities in the Provinces of Abruzzo: A Comparative Study Through the Indices of Deprivation and Principal Component Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Domenico Di Spalatro, Fabrizio Maturo and Lorella Sicuro 16 Expected Present and Final Value of an Annuity when some Non-Central Moments of the Capitalization Factor are Unknown: Theory and an Application using R . . . . . . . . . . . . . Salvador Cruz Rambaud, Fabrizio Maturo and Ana María Sánchez Pérez 17 Assessing the Effect of Financial Crisis of Earnings Manipulation. Empirical Evidence from the Top 1,000 World Listed Companies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Francesco Paolone and Matteo Pozzoli 18 Reasoning and Decision Making in Practicing Counseling . . . . . . . Antonio Maturo and Antonella Sciarra 19 Risks Associated with Reality: How Society Views the Current Wave of Migration; One Common Problem—Two Different Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ana Vallejo Andrada, Sarka Hoskova-Mayerova, Josef Krahulec and José Luis Sarasola Sanchez-Serrano
Recent Trends in Qualitative Theories for Economic and Social Sciences
20 Sociability and Dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . José Luis Sarasola Sánchez-Serrano, Ana Vallejo Andrada and Alberto Sarasola Fernandez
29 Some Aspects of Social Life in Romanian Villages in the Interwar Period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Daniel Flaut and Enache Tuşa
The book “Mathematical-Statistical Models and Qualitative Theories for Economic and Social Sciences” is part of the important series “Studies in Systems, Decision and Control” published by Springer. This is the result of a scientiﬁc collaboration, in the ﬁeld of economic and social systems, among experts from “University of Defence” in Brno (Czech Republic), “G. d’Annunzio” University of Chieti-Pescara (Italy), “Pablo de Olavide” University of Sevilla (Spain), and “Ovidius University” in Constanţa, (Romania). The ﬁrst part of the book deals with “Recent Trends in Mathematical and Statistical Models for Economic and Social Sciences,” whereas the second one concerns “Recent Trends in Qualitative Theories for Economic and Social Sciences.” The variety of the contributions developed in this book reflects the heterogeneity and complexity of economic and social phenomena; thus, a large spectrum of problems related to statistics, mathematics, teaching, social science, and economics has been presented in this volume. Therefore, a broad range of tools and techniques that may be used to solve problems on these topics has been presented in detail. Due to the wide range of topics of the presented research results, this peer-review book is addressed, in equal measure, to mathematicians, statisticians, sociologists, philosophers, and specialists in the ﬁelds of communication, social, and political sciences.
Recent Trends in Mathematical and Statistical Models for Economic and Social Sciences
Correlational Research of Expenditure Spend on Slovak Armed Forces Participation in Peace Support Operations Led by NATO Veronika Mitašová, Ján Havko and Tomáš Pavlenko
Abstract The expenditure which Ministry of Defence of the Slovak Republic spends on Armed Forces members’ participation in peace support operations led by the North Atlantic Treaty Organisation is dependent on many factors. The main aim of this chapter is to ﬁnd out the dependence level of this parameter from two selected factors, namely the level of defence expenditure and the GDP of the Slovak Republic. For this purpose the multifactor single-equation econometric model is created and tested. Based on the tests results, conclusions and proposals for further examination are formulated. Keywords Peace support operation model
Nowadays, peace support operations are an effective tool for conflict prevention and conflict resolution in problematic areas of the world. Mentioned type of operation is under the auspices of the international crisis management organizations. International organization of collective security, the North Atlantic Treaty Organisation (“NATO”), has undoubtedly a signiﬁcant place among them.
This contribution is focused on the assessment of factors, which affects participation of the Armed Forces of the Slovak Republic in NATO peace support operations. It is necessary to identify and understand what influences the amount of ﬁnance spent on these operations from state budget of the Slovak Republic (“the SR”). Based on the input data the multifactor single-equation econometric model is created and tested. According to the results of each test, the hypothesis, that the amount of the expenditure which Ministry of defence (“MoD”) of the SR spend on Armed Forces members’ participation in peace support operations led by NATO is dependent on the defence expenditures and GDP of the SR, is conﬁrmed or refuted.
Qualitative Analysis and Input Data
Before econometric model creation, it is necessary to do qualitative analysis, which means assessing relations between variables. In the contribution it will be veriﬁed, if the estimated correlation among the amount of ﬁnance spend on the Slovak Armed Forces members participation in NATO peace support operations, the defence expenditures and the level of GDP exists or not. It can be assumed, that the amount of ﬁnance, which states spend on participation of their armed forces in peace operations, is affected by a lot of factors. Table 1.1 shows some of them. For the purpose of creating and testing econometric model we should work with factors mentioned above, but because of many reasons, we will work only with data listed in the Table 1.2. First factor, variable x1, is defence expenditure of the SR. This kind of data is publicly available on the ofﬁcial website of MoD of the SR, but only since 2001. Second factor, variable x2—GDP of the SR, is available on the Eurostat portal. Third one, variable x3, could be number of completed and ongoing peace support operations led by NATO. Although the information about number of
Table 1.1 Factors affecting the amount of expenditure spend by MoD of the SR on Armed Forces members’ participation in peace support operations led by NATO Variable
Amount of expenditure spend by MoD of the SR on Armed Forces members’ participation in peace support operations led by NATO
Defence expenditure of the SR GDP of the SR Number of completed and ongoing peace support operations led by NATO Global security environment Number of military personnel in the SR Number of Slovak troops deployed in peace operations led by international crisis management organizations Costs of military personnel training Others
1 Correlational Research of Expenditure Spend on Slovak …
completed and ongoing operations is available, it is difﬁcult and also slightly mistakenly uses these data as a total number of peace support operations led by NATO in the individual year. Some operations are ongoing throughout the year, others only in certain months. More appropriate would be, in this case, to examine the correlation between the amount of expenditure spend by MoD of the SR on Armed Forces members’ participation in peace support operations led by NATO and the number of peace support operations during particular months. However, because of other data distribution, it is not possible. The same problem is in the case of another factor, variable x6—the number of Slovak troops deployed in peace operations led by international crisis management organizations. The number of troops in peace support operations may change through the operation, and this number is often slightly different from the mandate. Even though variable x4, which is global security environment, affects the amount of expenditure spend by MoD of the SR on Armed Forces members’ participation in peace support operations led by NATO, it is not a numerical quantity, so it would not be possible to use it in our econometric multifactor model. Other two variables, x5—the number of military personnel in the SR and x7—costs of military personnel training, would be appropriate to examine, but they are not available (Hošková-Mayerová 2017). The small range of data is influenced by the fact, that the SR is relatively young country, but also a lot of needed information are conﬁdential or they are not publicly available. Based on the data in the Table 1.2, it is possible to notice a growing trend of expenditure for peace support operations led by NATO. The expenditure had increased in 12 years more than nine times. A similar trend is in the development of
V. Mitašová et al.
GDP, which increased three times during the 12-year period. On the contrary, defence expenditures of the SR maintain approximately the same level.
The Construction of Econometric Model and Its Testing
It is possible to create and to test econometric model in different ways, from laborious and difﬁcult calculation through different software. The results in this contribution were gained through MS Ofﬁce Excel tools and STATISTICA software. Data sources were SIPRI database (Stockholm International Peace Research Institute) and Eurostat. The particular regression equation, which expresses the relation between dependent variable y (expenditure of MoD on participation of the Slovak Armed Forces in peace support operations led by NATO in million Euro) and explanatory variables x1 and x2 (defence expenditure at current prices in million Euro and GDP of the SR at current prices in million Euro), can be written in the form: y ∧ = 4.1035 − 0.0199x1 + 0.0007x2 + u
The value of the parameter b1 = −0.0199 indicates, that the increase of defence expenditure by 1 million Euro will reduce the amount of expenditure on the Slovak Armed Forces participation in NATO peace support operations by 19,900 Euro, while GDP remains unchanged. The value of the parameter b2 = 0.0007 indicates, that increase of GDP by 1 million Euro will increase the expenditure on the Slovak Armed Forces participation in NATO peace support operations by 700 Euro, providing defence expenditure remained unchanged. Multiple R = 0.8949 means, that there occurs a very strong positive correlation in the econometric model. The value of reliability R2 = 0.8008 can be interpreted, that about 80% of the explaining variable variability is explained by the variability of explanatory variables. Remaining 20% of the explaining variable variability, which is amount of expenditure spend by MoD of the SR on Armed Forces members’ participation in peace support operations led by NATO, is explained by other variables (Table 1.3). Graphical representation of variables y, x1, x2 distribution is in the Figs. 1.1, 1.2 and 1.3. On the right side of these ﬁgures are values characterizing variables, namely minimum, maximum, standard deviation or median.
Table 1.3 Basic statistical values of the econometric model
Summary statistics Multiple R Multiple R2 Adjusted R2
0.8949 0.8008 0.7566
1 Correlational Research of Expenditure Spend on Slovak …
Fig. 1.1 Graphical summary for variable y
Fig. 1.2 Graphical summary for variable x1
V. Mitašová et al.
Fig. 1.3 Graphical summary for variable x2
Econometric model must be tested after its creation, thus it is possible to conclude whether the model is applicable for practical needs. These tests are testing model as a whole through the coefﬁcient of determination R2 tested by Fisher’s statistics (F-statistic), testing parameters of variables through Student’s probability distribution (t-statistics), testing of residuals autocorrelation (we have <15 observations, so we will use Von-Neumann ratio and D-statistics). Veriﬁcation of heteroscedasticity, respectively homoscedasticity, is made by Goldﬁeld and Quandt test. The last test is used to ﬁnd out the presence of multicollinearity in the model. For this purpose, we will use Farrar and Glauber method, where the correlation matrix is tested through Chi-square (Mikolaj and Vančo 2004; Ristvej and Kampová 2009). Because of comprehensive testing procedures, there will be stated only particular resultant values of tests and conclusions related to them.
Testing of Econometric Model as a Whole
The value of determination coefﬁcient R2 is 0.8008. It means, that approximately 80% of the amount of expenditure spend by MoD of the SR on Armed Forces members’ participation in peace support operations led by NATO variability is explained by the variability of defence expenditure and GDP in the SR. Remaining nearly 20% of the explaining variable variability is affected by other factors, which
1 Correlational Research of Expenditure Spend on Slovak …
are not included in the model. F-statistic test was performed at a signiﬁcance level 0.05. Therefore, if the model would be signiﬁcant as a whole, the inequality (1.2) has to be valid. Fr > Fα; k; ½n − ðk + 1Þ
The value of Fr = 18.0938 and F0,05, 2, 9 = 4.2565, consequently, the determination coefﬁcient of on the signiﬁcance level 0.05 is considered as a signiﬁcant and the model as a whole is considered as a statistically signiﬁcant too.
Testing of Variables Parameters Through t-Statistics
Both of parameters, b1 = 0.0199 and b2 = 0, 0.0007, are tested at the signiﬁcance level 0.05. To consider parameter as a statistically signiﬁcant, the inequality (1.3) has to be valid. jti j > tα; ½n − ðk + 1Þ
In the case of parameter b1, after substituting into inequality 0.9811 < 2.2622, it does not apply. It means that the parameter b1 at the signiﬁcance level 0.05 is not considered as statistically signiﬁcant. After substituting into inequality in the case of parameter b2, inequality form is 5.2772 > 2.2622. Based on it, we can formulate conclusion that inequality applies, therefore, the parameter b2 at signiﬁcance level 0.05 is considered as statistically signiﬁcant.
Testing of Residuals Autocorrelation
Testing of residuals autocorrelation for <15 observations is carried out by Von-Neumann ratio. To autocorrelation veriﬁcation the calculated value is compared to the tabulated one, while the inequality (1.4) has to apply. D+ < D < D−
Value of D+ = 1.2301, D− = 3.1335 and D = 2.0705, therefore, the inequality applies. We conclude autocorrelation of residuals absents in our econometric model.
V. Mitašová et al.
Testing of Heteroscedasticity
It is necessary to test heteroscedasticity for each variable x (x1 and x2). For the hypothesis “scatter of residuals is constant, there is homoscedasticity of residuals in the model” acceptation, inequality (1.5) has to apply, whereby the value v means degree of freedom. F2, 1 ≤ Fαðv, vÞ
It is calculated according to Eq. (1.6). The value v = 2 and tabulated value F0.05;(2,2) = 19. v=½
ðn − M Þ − ðk + 1Þ 2
After substituting into inequality in the case of variable x1, it is 1.6852 < 19, in the case of variable x2, it is 1.4757 < 19. Therefore, the inequality applies in both cases, we conclude, that heteroscedasticity of residuals absents in our model. For better expression of values, in the Fig. 1.4 are shown predicted and observed values of variable y.
Fig. 1.4 Graph of predicted and observed values of variable y